Fractures as collections of cracks

A single fracture can be thought of as two rough surfaces in partial contact. Observations show that the noncontacting regions are patches of widely varying size and shape which are characterized by an aperture which is much less than any of the in-plane dimensions. A further idealization is therefore to assume that the regions of contact are welded and the noncontacting patches are replaced by cracks. The deformation of cracks arranged in simple two-dimensional (2-D) geometries can be described analytically. Solutions for noninteracting and interacting cracks are reviewed, and the analogy with solutions for ubiquitously cracked intact rock is discussed. Using the model of a fracture as a two-dimensional collection of cracks, expressions for fracture stiffness, flow of a single phase fluid through a fracture, and propagation of elastic waves across a fracture are formulated. Comparison with observations shows that this simple model provides a consistent description of many first order attributes of the mechanical deformation and fluid flow in fractures under normal stress, and the velocity and amplitude of seismic waves propagating in fractured rock. (C) 2000 Elsevier Science Ltd. All rights reserved.